Finite Group Databasebeta

← #18079987

Subgroups — #18079987

Order 4864.

644 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14569115C211yesmaximal, characteristic
2#14565992C211yesmaximal, characteristic, complemented
3#14562152C212yesmaximal
4#14561520C212yesmaximal, complemented
5C19×#1463C211yesmaximal, characteristic, complemented
6C2×#10597376C2211yescharacteristic
7C2×#10597372—21no—
8#11926483C412yescomplemented
9#11926461C412yescomplemented
10#11926434—22no—
11#11926423—21no—
12#11926423—21no—
13C4⋊C4×Dic19—24no—
14C4×C22⋊Dic19—21no—
15C4×C22⋊Dic19C2211yescharacteristic
16C4×C22⋊Dic19C2212yes—
17#11926279—24no—
18C22×C4⋊C4×C19C2211yescharacteristic
19C19×#407C2212yes—
20C19×#324—22no—
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C22×C22⋊D19—21no—
25C22×D76C2×C411yescharacteristic
26C2×M16×C19—22no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19C2×C412yes—
30C2×C4⋊C4×C19D412yes—
31C2×C22⋊Dic19—22no—
32C2×C22⋊Dic19—21no—
33#10597376—22no—
34#10597376—22no—
35C2×(C2×D19)⋊C4—22no—
36C2×(C2×D19)⋊C4—21no—
37C2×(C2×D19)⋊C4—22no—
38#10597372—28no—
39C2×C4⋊Dic19—22no—
40C2×C4⋊Dic19C2×C411yescharacteristic
41C2×C4×Dic19—22no—
42C2×C4×Dic19—22no—
43C2×C4×Dic19—22no—
44C2×C4×Dic19—21no—
45C19×C22⋊C8—22no—
46C19×C22⋊C8—22no—
47C19⋊#95—22no—
48C19⋊#95—22no—
49C19⋊#95—22no—
50C19⋊#95C2×C412yes—
51C19⋊#95D414yes—
52C24×C19C2×D411yescharacteristic
53C23×D19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—24no—
57C22×C4×C19—21no—
58C22×C4×C19—21no—
59C22×C4×C19—81no—
60C22×C4×C19—81no—
61C22×C4×C19C22⋊C412yes—
62C22×C4×C19C22⋊C412yes—
63C22×C4×C19C22×C411yescharacteristic
64C22×C4×C19C2×D412yes—
65C22×C4×C19C2×D411yescharacteristic
66C22×C4×C19#4112yes—
67C2×C22⋊D19—44no—
68C2×C22⋊D19—41no—
69C2×C22⋊D19—41no—
70C22×Dic19—24no—
71C22×Dic19—22no—
72C22×Dic19—21no—
73C2×D76—22no—
74C2×D76—81no—
75M16×C19—82no—
76C2×C8×C19—42no—
77C4⋊C4×C19—24no—
78C4⋊C4×C19—24no—
79C22⋊Dic19—28no—
80C22⋊Dic19—42no—
81(C2×D19)⋊C4—44no—
82(C2×D19)⋊C4—42no—
83(C2×D19)⋊C4—82no—
84C4⋊Dic19—28no—
85C4⋊Dic19—22no—
86C4×Dic19—28no—
87C4×Dic19—82no—
88C4×Dic19—82no—
89C4×Dic19—81no—
90#9410—191nomaximal, Sylow
91C23×C19—22no—
92C23×C19—22no—
93C23×C19—41no—
94C23×C19C2×C22⋊C411yescharacteristic
95C23×C19#12011yescharacteristic
96C23×C19#12311yescharacteristic
97C22×D19—42no—
98C22×D19—42no—
99C22×D19—41no—
100C22×D19—42no—
101C2×C4×C19—22no—
102C2×C4×C19—22no—
103C2×C4×C19—24no—
104C2×C4×C19—22no—
105C2×C4×C19—22no—
106C2×C4×C19—22no—
107C2×C4×C19—42no—
108C2×C4×C19—41no—
109C2×C4×C19—42no—
110C2×C4×C19—41no—
111C2×C4×C19—42no—
112C2×C4×C19—42no—
113C2×C4×C19—81no—
114C2×C4×C19#10414yes—
115C2×C4×C19C4×D412yes—
116C2×C4×C19#12112yes—
117C22⋊D19—82no—
118C22⋊D19—82no—
119C2×Dic19—28no—
120C2×Dic19—44no—
121C2×Dic19—44no—
122C2×Dic19—42no—
123C2×Dic19—42no—
124C2×Dic19—42no—
125C2×Dic19—41no—
126C2×Dic19—42no—
127D76—82no—
128C8×C19—82no—
129#2591—191no—
130#2274—191no—
131#1507—192no—
132#1463D1911yescharacteristic, complemented
133#1297—192no—
134C22×C19—21no—
135C22×C19—21no—
136C22×C19—21no—
137C22×C19—21no—
138C22×C19—21no—
139C22×C19—21no—
140C22×C19—21no—
141C22×C19—44no—
142C22×C19#38611yescharacteristic
143C22×C19C2×#10412yes—
144C22×C19#45412yes—
145C2×D19—84no—
146C2×D19—81no—
147C2×D19—81no—
148C2×D19—81no—
149C4×C19—24no—
150C4×C19—22no—
151C4×C19—22no—
152C4×C19—42no—
153Dic19—48no—
154Dic19—82no—
155Dic19—81no—
156C2×#121—191no—
157C2×#117—381no—
158C22×C4⋊C4C2×D1911yescharacteristic
159#407C2×D1912yes—
160#400—192no—
161#394—192no—
162#388—382no—
163#386—381no—
164#386—381no—
165C4×C4⋊C4—384no—
166C4×C22⋊C4—191no—
167C4×C22⋊C4—192no—
168C4×C22⋊C4—381no—
169#327—384no—
170#324—22no—
171C2×C19—22no—
172C2×C19—22no—
173C2×C19—41no—
174C2×C19#188811yescharacteristic
175C2×C19#189611yescharacteristic
176C2×C19#191311yescharacteristic
177D19—161no—
178C22×D4—191no—
179C22×D4—381no—
180C23×C4D7611yescharacteristic
181C23×C4D7611yescharacteristic
182C23×C4C22×D1911yescharacteristic
183C2×M16—22no—
184#121—382no—
185#121—382no—
186#117—388no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—191no—
190C2×C4⋊C4—382no—
191C2×C4⋊C4C4×D1912yes—
192C2×C4⋊C4C22⋊D1912yes—
193C2×C22⋊C4—382no—
194C2×C22⋊C4—381no—
195C2×C22⋊C4—382no—
196C2×C22⋊C4—381no—
197C2×C22⋊C4—382no—
198C2×C42—382no—
199C2×C42—382no—
200C2×C42—382no—
201C2×C42—381no—
202C22⋊C8—22no—
203C22⋊C8—22no—
204#95—192no—
205#95—194no—
206#95—382no—
207#95—382no—
208#95—382no—
209C19#941011yescharacteristic, complemented, Sylow
210C24—381no—
211C24C2×D7611yescharacteristic
212C2×D4—382no—
213C2×D4—764no—
214C2×D4—761no—
215C2×D4—761no—
216C2×D4—1521no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—24no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—81no—
223C22×C4—81no—
224C22×C4—384no—
225C22×C4—382no—
226C22×C4—381no—
227C22×C4(C2×D19)⋊C412yes—
228C22×C4(C2×D19)⋊C412yes—
229C22×C4C2×C4×D1911yescharacteristic
230C22×C4D4×D1912yes—
231C22×C4#6454312yes—
232C22×C4C2×C22⋊D1911yescharacteristic
233M16—82no—
234C2×C8—42no—
235C4⋊C4—24no—
236C4⋊C4—24no—
237C4⋊C4—388no—
238C4⋊C4—382no—
239C22⋊C4—388no—
240C22⋊C4—762no—
241C22⋊C4—762no—
242C22⋊C4—764no—
243C22⋊C4—1522no—
244C42—388no—
245C42—1522no—
246C42—1521no—
247C42—1522no—
248C23—22no—
249C23—22no—
250C23—41no—
251C23—762no—
252C23—762no—
253C23—762no—
254C23—761no—
255C23#1059732811yescharacteristic
256C23#1059733211yescharacteristic
257C23C2×(C2×D19)⋊C411yescharacteristic
258D4—1522no—
259D4—1522no—
260D4—1522no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—388no—
275C2×C4—764no—
276C2×C4—764no—
277C2×C4—762no—
278C2×C4—762no—
279C2×C4—762no—
280C2×C4—762no—
281C2×C4—761no—
282C2×C4#1059728214yes—
283C2×C4(C22⋊D19)⋊C412yes—
284C2×C4#1059738512yes—
285C8—82no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—44no—
294C22—1524no—
295C22—1521no—
296C22—1521no—
297C22—1521no—
298C22#1192642111yescharacteristic
299C22C2×#1059728212yes—
300C22#1192671912yes—
301C4—22no—
302C4—22no—
303C4—24no—
304C4—42no—
305C4—768no—
306C4—1522no—
307C4—1521no—
308C2—22no—
309C2—22no—
310C2—41no—
311C2—3041no—
312C2#1456403611yescharacteristic
313C2#1456407611yescharacteristic
314C2#1456417511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1463C2
socleC22×C19#386
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1463D19
hypocenterC19#9410
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14565992C2semidirect
4. #14561520C2semidirect
5. C19×#1463C2semidirect
8. #11926483C4semidirect
9. #11926461C4semidirect
132. #1463D19semidirect
209. C19#9410semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145691152
#145659922
#145621522
#145615202
C19×#14632
#941019